**3.2 Basalt as the host rock**

Basaltic caves (often as tubes) were formed in the process of the viscous lava flow, for example, Wudalianchi ice cave. Mechanical stability of lava tubes depends on their size (diameter), buried depth, and geometry in the cooling period. We conducted a series of two-dimensional thermo-elastic finite element calculations to estimate the effects of these three controlling factors [25].

**Figure 4** shows the principle stress distributions around a lava tube of diameter 10 m at the last computing time step. It can be seen from **Figure 4a** that the largest maximum principal stress is at the top and bottom sides of the lava tube, and it is tensile stress. The left and right sides are also tensile stresses, but the magnitude is much smaller. **Figure 4b** is the minimum principal stress distribution. Obviously, the minimum principal stress of the upper and lower sides of the lava tube is tensile stress, while that of the left and right sides is compressive stress, and the magnitude of the stress around the lava tube is equal. These modeling results reveal that the most vulnerable place of the lava tube is on the top and bottom, and the rupture type is tension rupture.

We investigated three controlling factors (diameter, depth, and geometry) of lava tubes in the cooling period by FEM method, and the modeling results were illustrated in **Figure 5**. At the last time step, maximum principal stress of **Figure 5a** (normal lava tube) is smaller than that of **Figure 5b** (bigger lava tube), implying bigger lava tubes were easier ruptured. Similarly, lave tubes with larger buried

#### **Figure 4.**

*Principle stress distributions around the lava tube. (a) Maximum principal stress and (b) minimum principal stress (modified from [25]).*

#### **Figure 5.**

*Maximum principal stresses at the top (dashed line) and bottom (solid line) side of a normal (a), a bigger (b), a deeper (c), and an elliptical (d) lava tube, respectively. The normal lava tube with 10 m diameter and 5 m buried depth. The bigger lava tube with 16 m diameter and 5 m buried depth. The deeper lava tube with 10 m diameter and 8 m buried depth. The elliptical lave tube with 12 m long axis, 8 m short axis, and 5 m buried depth (modified from [25]).*

depth would be easier ruptured than normal ones (**Figure 5c**). Elliptical lava tubes would be more stable than normal lava tubes (**Figure 5d**).
